scholarly journals Selection of Random Walkers that Optimizes the Global Mean First-Passage Time for Search in Complex Networks

2017 ◽  
Vol 108 ◽  
pp. 2423-2427 ◽  
Author(s):  
Mu Cong Ding ◽  
Kwok Yip Szeto
Keyword(s):  
Complex Networks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Random Walkers ◽  
Global Mean ◽  
Selection Of

scholarly journals Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Zhongtuan Zheng ◽  
Gaoxi Xiao ◽  
Guoqiang Wang ◽  
Guanglin Zhang ◽  
Kaizhong Jiang
Keyword(s):  
Complex Networks ◽  
Random Walks ◽  
First Passage Time ◽  
Network Models ◽  
Passage Time ◽  
Main Role ◽  
Mean First Passage Time ◽  
Eigenvalues And Eigenvectors ◽  
First Passage ◽  
The Mean

This paper investigates, both theoretically and numerically, preferential random walks (PRW) on weighted complex networks. By using two different analytical methods, two exact expressions are derived for the mean first passage time (MFPT) between two nodes. On one hand, the MFPT is got explicitly in terms of the eigenvalues and eigenvectors of a matrix associated with the transition matrix of PRW. On the other hand, the center-product-degree (CPD) is introduced as one measure of node strength and it plays a main role in determining the scaling of the MFPT for the PRW. Comparative studies are also performed on PRW and simple random walks (SRW). Numerical simulations of random walks on paradigmatic network models confirm analytical predictions and deepen discussions in different aspects. The work may provide a comprehensive approach for exploring random walks on complex networks, especially biased random walks, which may also help to better understand and tackle some practical problems such as search and routing on networks.

scholarly journals Determining global mean-first-passage time of random walks on Vicsek fractals using eigenvalues of Laplacian matrices

2010 ◽  
Vol 81 (3) ◽  
Author(s):  
Zhongzhi Zhang ◽  
Bin Wu ◽  
Hongjuan Zhang ◽  
Shuigeng Zhou ◽  
Jihong Guan ◽  
...  
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Laplacian Matrices ◽  
Global Mean

scholarly journals Optimizing the First-Passage Process on a Class of Fractal Scale-Free Trees

2021 ◽  
Vol 5 (4) ◽  
pp. 184
Author(s):  
Long Gao ◽  
Junhao Peng ◽  
Chunming Tang
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Exact Result ◽  
Passage Time ◽  
Target Site ◽  
Mean First Passage Time ◽  
First Passage ◽  
Scale Free ◽  
Global Mean ◽  
Biased Random Walks

First-passage processes on fractals are of particular importance since fractals are ubiquitous in nature, and first-passage processes are fundamental dynamic processes that have wide applications. The global mean first-passage time (GMFPT), which is the expected time for a walker (or a particle) to first reach the given target site while the probability distribution for the position of target site is uniform, is a useful indicator for the transport efficiency of the whole network. The smaller the GMFPT, the faster the mass is transported on the network. In this work, we consider the first-passage process on a class of fractal scale-free trees (FSTs), aiming at speeding up the first-passage process on the FSTs. Firstly, we analyze the global mean first-passage time (GMFPT) for unbiased random walks on the FSTs. Then we introduce proper weight, dominated by a parameter w(w>0), to each edge of the FSTs and construct a biased random walks strategy based on these weights. Next, we analytically evaluated the GMFPT for biased random walks on the FSTs. The exact results of the GMFPT for unbiased and biased random walks on the FSTs are both obtained. Finally, we view the GMFPT as a function of parameter w and find the point where the GMFPT achieves its minimum. The exact result is obtained and a way to optimize and speed up the first-passage process on the FSTs is presented.

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